Question

Дано вектори а(4;2) і b (х;-4).При якому значенніх ці вектори колінеарні.

Answer 1

вектори колінеарні, якщо відповідні координати пропорційні

 

4/x=2/(-4)

x=4*(-4)/2=-8

Answer 2

Given Vectors:

The given vectors are a(4,2) and b(x,-4).

Collinearity of Vectors:

Two vectors are said to be collinear if they are scalar multiples of each other. In other words, if one vector can be obtained by multiplying the other vector by a scalar, then they are collinear.

To determine the values of x for which the vectors a and b are collinear, we need to find the scalar value that makes the two vectors proportional.

Let's set up the proportion:

a(4,2) = k * b(x,-4)

where k is the scalar value.

To find the value of x, we can equate the corresponding components of the vectors:

4 = k * x (equation 1) 2 = k * (-4) (equation 2)

Solving equation 2 for k, we get:

k = 2 / (-4) = -1/2

Substituting this value of k into equation 1, we can solve for x:

4 = (-1/2) * x

Multiplying both sides by -2:

-8 = x

Therefore, the vectors a(4,2) and b(-8,-4) are collinear when x = -8.

Conclusion:

The vectors a(4,2) and b(x,-4) are collinear when x = -8.